Einstein field equations (briefly, \(\mathbf {EFE}\) ) is unfit to outline the late-time inflation of the universe without assuming the presence of a couple of undetectable components that should supply the cause for the dark matter and the dark energy. This is the major motivation for extending it to obtain a few of higher-order field equations of gravity. It's worth noting that \(f(\mathcal {R})\) -gravity is an intrinsic extension, rather than a generalization, of Einstein's gravity, in which the Hilbert-Einstein action of the gravitational field is replaced by a function \(f(\mathcal {R})\) , where \(\mathcal {R}\)  is the Ricci scalar. The preceding theory was introduced by Buchdahl in 1970 [1]}, and it achieved viability with Starobinsky's [2]} investigations of cosmic inflation. Various useful functional representations of \(f(\mathcal {R})\)  have been proposed in the literature, for more details see ([3]}, [4]}, [5]}, [6]}).
